1. Field of the Invention
The present invention relates to a method for simulating compositional and/or multiphase transfers between the porous matrix and the fractures of a fractured multilayer porous medium.
2. Description of the Prior Art
The prior art to which reference is made hereafter is defined and explained in the following publications:                Chen, W. H., M. L. Wasserman and R. E. Fitzmorris 1987. A Thermal Simulator for Naturally Fractured Reservoirs. Paper SPE 16008 presented at the 9th SPE Symposium on Reservoir Simulation held in San Antonio, Tex., Feb. 1-4, 1987;        Gilman, J. R. 1986. An Efficient Finite-Difference Method for Simulating Phase Segregation in the Matrix Blocks in Double-Porosity Reservoirs. SPE Reservoir Engineering, July 1986. Pages 403-413;        Kazemi, H., Merrill, L. S., Porterfield, K. L. and Zeman, P. R. 1976. Numerical Simulation of Water-Oil Flow in Naturally Fractured Reservoirs. SPE Journal, December 1976, 317;        Pruess, K. and T. N. Narasimhan 1985. A Practical Method for Modelling Fluid and Heat Flow in Fractured Porous Media. Society of Petroleum Engineers Journal, February 1985. Pages 14-26;        Quintard, M. and Whitaker, S. 1996. Transport in Chemically and Mechanically Heterogeneous Porous Media. Advances in Water Resources, 19(1), 29-60;        Sabathier, J. C., B. J. Bourbiaux, M. C. Cacas and S. Sarda 1998. A New Approach of Fractured Reservoirs. Paper SPE 39825 presented at the SPE International Petroleum Conference and Exhibition of Mexico held in Villahermosa, Mexico, 3-5 Mar. 1998;        Saïdi, A. M. 1983. Simulation of Naturally Fractured Reservoirs. Paper SPE 12270 presented at the 7th SPE Symposium on Reservoir Simulation held in San Francisco, Calif., Nov. 15-18, 1983; and        Warren, J. E. and P. J. Root 1963. The Behavior of Naturally Fractured Reservoirs. Society of Petroleum Engineers Journal, September 1963. Pages 245-255.        
Furthermore, various methods for simulating flows in fractured media are the subject of French patent 2,809,894 filed by the assignee and in French patent applications 02/03,436 and 03/01,090.
Reliable estimations concerning a fractured reservoir in terms of productivity and recovery require a multidisciplinary approach in order to minimize the uncertainties linked with modelling of the fracture network and simulation of the multiphase flow. In particular, the following three stages play a determinant part:
1. Construction of a model representative of natural fracture networks from available field data;
2. Conversion of this geologic model to an equivalent double porosity model; and
3. Obtaining a good estimation of the involved physical production mechanisms and reproduction thereof by means of the multiphase double porosity simulator.
The method described hereafter deals with the third stage, and more precisely with a type of formulation suited for simulation of the complex matrix-fracture transfers, that is multiphase and/or compositional and sometimes thermal transfers involved in most gas injection recovery processes. In fact, the predictions of a double porosity simulator are extremely sensitive to the formulation of the matrix-fracture transfers insofar as the major part of the oil in place is located in the matrix medium.
The double porosity conceptual model represents the fractured reservoir in a form of a set of parallelepipedic matrix blocks limited by a set of uniform orthogonal fractures (FIG. 1). Two superposed grids representing the two media, fracture and matrix, are used for flow calculation. The fracture flows are calculated between grid cells of the fracture grid, the matrix-fracture transfers are calculated for each pair of the superposed matrix and fracture cells, and the flows within the matrix are also taken into account in the double porosity option of these simulators. Warren and Root proposed the following expression for the matrix-fracture flow (per matrix volume unit) by referring to a single-phase transfer on quasi-stationary flow controlled by the pressure diffusivity:
                              f          p                =                  σ          ⁢                                          ⁢          K          ⁢                      1            μ                    ⁢                      (                                          p                m                            -                              p                f                                      )                                              (        1        )            where pm and pf are the mean matrix and fracture pressures. This equation comprises a proportionality constant σ referred to as form factor (dimension: 1/L2), which reflects the geometry of the non-discretized matrix block of dimensions (Lx,Ly,Lz). Kazemi proposed the following expression for σ:
                    σ        =                              4                          L              x              2                                +                      4                          L              y              2                                +                      4                          L              z              2                                                          (        2        )            
The mass transfer (mass flow per matrix volume unit) due to the molecular diffusion is expressed in a similar way:
                              f          d                =                  σ          ⁢                                          ⁢          D          ⁢                      ϕ            τ                    ⁢                      ρ            ⁡                          (                                                C                  m                                -                                  C                  f                                            )                                                          (        3        )            where D is the diffusion coefficient, φ the porosity, τ the tortuosity factor, ρ the fluid density and C the concentration of the components in the fluid.
Extension of these expressions to multiphase flows leads to difficulties linked with the representation of a transient phenomenon that is difficult to reproduce without discretizing the matrix block.
This is the reason why discretization of the matrix blocks was proposed (See Saïdi, 1983) and introduced in certain simulators (See Pruess et al., (1985) or Gilman, (1986) or Chen et al., (1987)). This approach is satisfactory but it involves computation requirements that cannot be satisfied for complex or large-size reservoir models. Therefore, within the scope of the present invention, the practical situation is kept wherein the matrix blocks are not discretized and the matrix-fracture transfers are represented by a single source term expressed as a function of the matrix/fracture properties and of variables (pressures, saturations, compositions).
The difficulties increase further in the case of multiphase transfers of fluids under thermodynamic disequilibrium because the mass transfer of the components occurs at the interface between the phases and adds to the convective and diffusive transfers which take place within each phase.
To date, no double porosity simulator capable of reliably simulating multiphase compositional transfers between a matrix block filled with oil and a fracture filled with gas at disequilibrium is known, except if a convective process (gravity for example) initiates transfer of the gas to the matrix. In fact, in such situations, the gaseous components must first be dissolved in the oil phase of the matrix until the latter is entirely saturated with gas and a gas phase appears in the matrix block. It is only at this stage that the fracture-matrix single-phase molecular diffusion process can be initiated in the simulation.